A slang term, "He knew all the angles", meaning he was streetwise. This usage is heard in the opening sequence of Woody Allen's famous movie Manhattan.
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Angles provide a means ofexpressing the difference in slope between two rays meeting at a vertex without the needto explicitly define the slopes of the two rays.
The first concept was used by Eudemus, who regarded an angle as a deviation from astraight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclidadopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.
Since thecircumference of a circle is always directly proportional to the length of its radius, the measure of the angle is independent ofthe size of the circle.
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